## Definition: a three-sided polygon with a sum of 180 degrees in the angle measures Example: A triangle is a shape with only three sides and is also known as a polygon

### A triangle is a polygon with three sides and three angles

A triangle is a polygon with three sides and three angles. It is one of the most basic and fundamental shapes in geometry. The sum of the three angles in a triangle is always 180 degrees.

In a triangle, the sides can have different lengths and the angles can have different measures. Triangles can be classified based on the lengths of their sides and the measures of their angles.

Based on the lengths of the sides, triangles can be classified as follows:

1. Scalene triangle: A triangle with all three sides of different lengths.

2. Isosceles triangle: A triangle with two sides of the same length.

3. Equilateral triangle: A triangle with all three sides of the same length.

Based on the measures of the angles, triangles can be classified as follows:

1. Acute triangle: A triangle with all three angles measuring less than 90 degrees.

2. Obtuse triangle: A triangle with one angle measuring greater than 90 degrees.

3. Right triangle: A triangle with one angle measuring 90 degrees. In a right triangle, the side opposite to the right angle is called the hypotenuse.

Triangles also have various properties and formulas related to their sides and angles, such as the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

When working with triangles, it is important to apply the appropriate formulas and theorems to solve specific problems and find missing information such as angles or side lengths.

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